PISA in Practice:
Cognitive Activation in Maths
How to use it in the classroom
PISA in Practice: Cognitive Activation in Maths
Foreword
The OECD Programme for International Student Assessment – or PISA - is used by
governments around the world to compare results of differing education policies and
provides a wealth of information which informs educational policy.
Yet this evidence is not the sole preserve of policy makers. In-depth analysis of the
PISA data can help inform practitioners and school leaders about factors relating to
pupil achievement. Such analysis can, for example, provide robust, useful evidence
about whether specific teaching practices are related to achievement, and whether that
relationship is the same for all pupils, regardless of ability.
It is not enough, though, to simply identify where such relationships exist – it is important
to reflect on how practitioners could introduce these into their lessons and embed them in
ongoing classroom practice.
In this series, commissioned by the Department for Education (DfE), we showcase some
findings from PISA which teachers can use in the classroom.
This report shines a spotlight on the teaching practice of Cognitive Activation, explores
how this practice is related to achievement, and identifies short, medium and long-term
strategies for using Cognitive Activation in the teaching of mathematics.
PISA 2012 in England was conducted by NFER on behalf of the Department for Education
(DfE) The national report for England can be accessed at: https://www.gov.uk/government/
publications/programme-for-international-student-assessment-pisa-2012-national-reportfor-england; and the international reports at: http://www.OECD.org/PISA
Bethan Burge, Research Director
Published in June 2015
By the National Foundation for Educational Research,
The Mere, Upton Park, Slough, Berkshire SL1 2DQ
www.nfer.ac.uk
© 2015 National Foundation for Educational Research
Registered Charity No. 313392
ISBN 978-1-910008-36-2
How to cite this publication:
Burge, B., Lenkeit, J. and Sizmur, J. (2015).
PISA in Practice: Cognitive Activation in Maths. Slough: NFER.
PISA in Practice: Cognitive Activation in Maths
Contents
Overview
2
Introduction: Cognitive Activation4
How often do maths teachers use Cognitive Activation
strategies in their lessons?
Cognitive Activation and pupil ability
5
7
Cognitive Activation and achievement11
Cognitive Activation and family background
11
Cognitive Activation and pupil attitudes to learning maths12
Summary
15
What can I do to increase the amount of Cognitive Activation in my lessons?
16
References
18
Page 1
PISA in Practice: Cognitive Activation in Maths
Overview
What is Cognitive Activation?
Cognitive Activation is, in essence, about teaching pupils strategies, such as summarising,
questioning and predicting, which they can call upon when solving maths problems. Such
strategies encourage pupils to think more deeply in order to find solutions and to focus on
the method they use to reach the answer rather than simply focusing on the answer itself.
Some of these strategies will require pupils to link new information to information they have
already learned. Making connections between mathematical facts, procedures and ideas,
will result in enhanced learning and a deeper understanding of the concepts.
Give pupils maths problems
that require them to think for
an extended time
Encourage pupils to
reflect on problems
Ask pupils to use
their own procedures
for solving complex
problems
Create a learning
community where pupils are
able to learn from mistakes
Give pupils problems
with no immediately obvious
method of solution or
multiple solutions
Present pupils with
problems in different
contexts and ask them to
apply what they have learned
to new contexts
Ask pupils to explain
how they solved a problem
and why they chose
that method
Page 2
PISA in Practice: Cognitive Activation in Maths
Why is it an important teaching practice?
• Cognitive Activation is significantly
associated with higher mathematics
achievement.
• Pupils with low and medium socioeconomic status (SES) profit most from
higher levels of Cognitive Activation in
their maths lessons.
• In England, pupils report that their
maths teacher asks them to use
Cognitive Activation strategies to solve
problems more often than is the
case internationally.
• Cognitive Activation is positively related
to a number of pupil characteristics that
are linked to achievement (motivation,
self-efficacy and self-concept).
• There are significant differences in the
frequency with which pupils of different
abilities use Cognitive Activation
strategies in their maths lessons.
• For pupils with low SES a higher level
of Cognitive Activation in their maths
lessons is accompanied by higher
self-efficacy.
• For the majority of pupils, a higher level of
Cognitive Activation in their maths lessons
is accompanied by lower maths anxiety.
How can I make it part of my practice?
NEXT LESSON
Relate your lesson to a real
life scenario, for example:
− What statistics do you
come across in everyday
life? Why is it important to
understand how to interpret
statistics used in the media?
Model key Cognitive
Activation strategies and
encourage pupils to use these
techniques, for example:
− Punctuate the discussion
with questions like: ‘What
if…?’; ‘Does everyone think
that…?’; ‘Might there be an
alternative way…?’
Listen – be prepared to adapt
your lesson plan. Use the
evidence of what you hear
and see to ensure you are
meeting learners where they
are, differentiating their range
of learning needs.
NEXT TERM
Encourage your
pupils to identify
how particular maths
concepts can be
applied in a range of
situations and use
their suggestions as
a basis for planning
subsequent lessons.
Encourage a culture
of exploratory talk in
your classroom. Ask
pupils to consider
a range of possible
solutions to problems
and identify, for
themselves, what
they need to learn.
Speak to your pupils
about the Cognitive
Activation strategies
you are using in
your lessons, are
there any that they
find particularly
challenging and if
so why?
Discuss with
colleagues your
observations of
how the Cognitive
Activation strategies
you are using are
working and any
particular difficulties
you have had.
NEXT YEAR
Consider collaborative
planning to develop and
share a range of Cognitive
Activation strategies to help
ensure they are being used
across different ability groups.
Hold regular update
meetings so that colleagues
can continue to share, inspire
and maintain awareness of
the importance of Cognitive
Activation for enhancing
learning.
Page 3
Consider the development
of interdisciplinary units
where learning is linked to
real life situations across
subject areas.
PISA in Practice: Cognitive Activation in Maths
Introduction: Cognitive Activation
The three most basic dimensions of quality teaching have been described as:
• clear, well-structured classroom management
• supportive, student-oriented classroom climate
• cognitive activation with challenging content (Klieme et al., 2009).
This report focuses on the third of these basic dimensions, Cognitive Activation, and
explores the link between Cognitive Activation and maths achievement.
There has been much research on the relationship between the level of challenge pupils
receive in their lessons and their achievement. In his extensive study of factors relating to
student achievement, Hattie (2009) describes quality teachers as those who challenge their
pupils. Specifically, instructional processes that teach pupils cognitive strategies and require
them to summarise, question, clarify and predict appear to be
particularly important for learning. Further support for
this finding comes from OECD’s international survey
of teaching and learning (TALIS) which notes that
in order to foster cognitive activity teachers
need to use deep and challenging content
The Programme for International Student
(Mayer, 2004; Brown, 1994). It appears that
Assessment (PISA) is the world’s biggest
argumentation and non-routine problem
international education survey, involving schools
solving in particular develop pupils’
and pupils in over 60 countries.
ability to make connections between
mathematical facts, procedures, ideas
It assesses the knowledge and skills of 15-year-olds
and representations (Hiebert and Grouws,
in maths, science and reading and was developed
2007; OECD, 2012).
jointly by member countries of the Organisation
What is PISA?
for Economic Co-operation and Development
In PISA, Cognitive Activation is identified
(OECD). Maths was the main subject in PISA
as one of several practices that support
2012. In addition pupils and schools completed
the development of mathematical literacy
questionnaires to provide information about
(OECD, 2013). In PISA 2012, OECD sought
pupil background and attitudes, and
to find out how often pupils were exposed
aspects of school management
to activities in their maths lessons that would
and school climate
be cognitively activating. This report uses data
respectively.
from PISA 2012 to explore the relationship between
Cognitive Activation and achievement in England.
Page 4
PISA in Practice: Cognitive Activation in Maths
How often do maths teachers use Cognitive
Activation strategies in their lessons?
As Cognitive Activation has been shown to support the development of mathematical
literacy it is important to examine how often pupils in England use Cognitive Activation
strategies to solve problems in their maths lessons and whether this varies across pupils of
different abilities.
Pupils were asked, in the PISA Student Questionnaire, how often their maths teacher asks
them to use a number of specific Cognitive Activation strategies to tackle maths problems
in their lessons. This included asking pupils to reflect on problems, solve complex problems
and apply knowledge to new contexts. They had to report whether the teacher used these
strategies: ‘never or rarely ’, ‘sometimes’, ‘often’ or ‘always or almost always’.
Cognitive Activation in PISA
The teacher…
…encourages us to reflect on problems.
…gives problems that require us to think for an extended time.
…asks us to use our own procedures for solving complex problems.
…presents problems with no immediately obvious method of solution.
…presents problems in different contexts.
…helps us to learn from mistakes we have made.
…asks us to explain how we have solved a problem.
…asks us to apply what we have learned to new contexts.
…gives problems with multiple solutions.
In England, pupils report that their maths teacher asks them to use Cognitive Activation
strategies to solve problems more often than is seen on average internationally1. For all
of the strategies listed above, greater proportions of pupils in England reported that they
occurred often, almost always, or always in their maths lessons (Wheater et al., 2013). The
strategy teachers used most often was asking pupils to explain how they had solved a
problem, over 80 per cent of pupils reported that their teacher did this frequently. A high
proportion of the pupils reported that their teacher gave them problems which required them
to apply their learning to new contexts or presented problems in different contexts.
This suggests that teachers recognise the importance of having a more conceptual
understanding rather than relying solely on surface knowledge or rote learning. However,
less than half of pupils reported that teachers frequently asked them to decide on their
own procedure for solving problems. This may reflect an issue identified by Hattie (2009) as
‘knowledge telling’, this refers to the observation that teachers spend a lot of lesson time
telling pupils pieces of information. Therefore, although the data suggests that teachers
frequently encourage their pupils to apply their understanding in new and different contexts,
it is possible that for many pupils the understanding they are applying is something they
have been told by the teacher rather than their own solution to a problem.
This refers to the OECD average. This is the mean of the data values for all OECD countries for which data are available or can be
estimated. The OECD average can be used to see how a country compares on a given indicator with a typical OECD country
(OECD, 2005).
1
Page 5
PISA in Practice: Cognitive Activation in Maths
Table 1: Frequency of Cognitive Activation strategies in maths lessons
Thinking about the mathematics teacher who taught your last mathematics lesson,
how often does he or she do each of the following?
often, almost always or always
All
Low
Medium
High
pupils
ability
ability
ability
The teacher asks questions that make us
reflect on the problem.
The teacher gives us problems that require
us to think for an extended time.
The teacher asks us to decide on our own
procedures for solving complex problems.
The teacher presents problems which have
no immediately obvious method for finding
the answer.
The teacher presents problems in different
contexts so that students know whether
they have understood the concepts.
The teacher helps us to learn from mistakes
we have made.
The teacher asks us to explain how we have
solved a problem.
The teacher presents problems that require
students to apply what they have learned to
new contexts.
The teacher gives us problems that can be
solved in several different ways.
Page 6
69%
68%
66%
73%
72%
62%
72%
78%
46%
45%
44%
50%
59%
43%
58%
66%
67%
60%
68%
72%
78%
77%
78%
79%
83%
76%
83%
86%
73%
62%
74%
81%
66%
65%
67%
65%
PISA in Practice: Cognitive Activation in Maths
Cognitive Activation and pupil ability
PISA defines ability in terms of proficiency levels. The proficiency levels describe the
types of skills pupils are likely to demonstrate and the tasks that they are able to complete
(OECD, 2014). Test questions that focus on simple tasks, involving familiar contexts where
all relevant information is present, are categorised at lower levels. Questions that are more
demanding, that require pupils to develop and work with models for complex situations,
identifying constraints and specifying assumptions, are categorised at higher levels. Pupils
described as being at a particular level not only demonstrate the knowledge and skills
associated with that level but also the proficiencies required at lower levels.
Based on these proficiency levels, we categorised pupils as low ability, medium ability and
high ability. In England, 17 per cent of pupils are categorised as low ability, 42 per cent as
medium ability and 41 per cent as high ability.
As shown in Table 1, there are some differences across the ability groups in terms of the
frequency with which they report their teachers using a number of Cognitive Activation
strategies. On average, high ability pupils report being given cognitively activating tasks in
their maths lessons significantly more often than the medium and low ability pupils. The low
ability pupils report undertaking cognitively activating tasks least often.
• Low ability pupils report that their teacher gives them problems that require them
to think for an extended time; asks them to apply what they learned; presents
problems in different contexts and asks the pupils for explanations significantly less
often than the medium or high ability pupils.
• High ability pupils report that their teacher encourages them to reflect on problems
and presents them with problems that have no obvious solution significantly more
often than the low and medium ability pupils. These latter groups report being given
these types of problems with similar frequency.
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PISA in Practice: Cognitive Activation in Maths
Ability level
What pupils can typically do
• conceptualise, generalise and utilise information based on their
investigations and modelling of complex problem situations
• link different information sources and representations and flexibly
translate among them
• advanced mathematical thinking and reasoning
• possess a mastery of symbolic and formal mathematical
operations and relationships, and develop new approaches and
strategies for attacking novel situations
High
ability
• reflect on their actions, and formulate and precisely communicate
their actions and reflections
• develop and work with models for complex situations, identifying
constraints and specifying assumptions
• select, compare, and evaluate appropriate problem-solving
strategies for dealing with complex problems
• work strategically using broad, well-developed thinking and
reasoning skills
• begin to reflect on their work and formulate and communicate their
interpretations and reasoning
• work effectively with explicit models for complex concrete situations
• select and integrate different representations, including symbolic,
linking them directly to aspects of real-world situations
• utilise their limited range of skills and reason with some insight
• construct and communicate explanations and arguments
• execute clearly described procedures, including those that require
sequential decisions
• articulate interpretations that are sufficiently sound to be a base for
building a simple model
Medium
ability
• interpret and use representations based on different information
sources and reason directly from them
• handle percentages, fractions and decimal numbers and work with
proportional relationships
• interpret and recognise situations in contexts that require no more
than direct inference
• extract relevant information from a single source
• employ basic algorithms, formulae, procedures, or conventions to
solve problem
• answer questions involving familiar contexts where all relevant
information is present
Low
ability
• identify information and to carry out routine procedures according
to direct instructions in explicit situations
• perform actions that are almost always obvious and follow
immediately from the given stimuli
Source: Adapted from OECD (2014), p.61
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PISA in Practice: Cognitive Activation in Maths
The biggest differences are seen between the high and low ability pupils. This finding
suggests that teachers may not feel that lower ability pupils have a sufficient level of basic
mathematical knowledge to approach more cognitively demanding tasks. The most notable
difference is seen for the following strategy: The teacher presents problems which have no
immediately obvious method for finding the answer. Twenty per cent more high ability pupils
reported that their teacher used this strategy frequently in maths lessons. It is possible that
teachers may not believe lower ability pupils are able to cope with the cognitive demand of
solving a problem in this way or these pupils may not have access to a variety of solution
methods and therefore this could become a de-motivating activity. A sizable difference is
also seen for the strategies that involve pupils applying their knowledge and understanding
in new or different contexts. This may be a result of the fact that teachers of lower ability
pupils have to spend more time ensuring that pupils have understood the ‘basics’ and may
not have time to spend working in different contexts before they need to move on to the
next topic.
There was no difference between the ability groups in terms of how often they report that
their teacher helps them learn from their mistakes. This suggests that teachers may feel that
pupils of all abilities can be helped to learn from their mistakes. As Hattie (2009) points out
it is not just low ability pupils that make errors, pupils of all abilities do not always succeed
the first time and therefore for all pupils there will be opportunities to learn from mistakes.
Understanding the mistakes we make is a critical step in understanding what we need to do
to improve and become successful.
Page 9
PISA in Practice: Cognitive Activation in Maths
Cognitive Activation and achievement
Cognitive Activation is significantly related to higher maths achievement across all pupils.
This means that pupils who are more frequently given tasks which require them to
summarise, question, clarify and predict, in their maths lessons have higher mean maths
scores in PISA. However, as we have seen in the previous section, higher ability pupils
report that their teachers use Cognitive Activation strategies more frequently than less able
pupils. Therefore it is difficult to say whether the use of these strategies results in higher
achievement or whether higher achievement is the result of higher ability pupils using these
strategies more frequently in their lessons.
Cognitive Activation and
family background
This section explores the link between Cognitive
Activation and maths achievement in PISA 2012
for pupils from different family backgrounds. PISA
asks pupils a range of questions about their family
background. This information is used to create a
measure of economic, social and cultural status
(ESCS index). For this report we sorted pupils three
groups (low, medium and high ESCS) based on
their responses to the questions.
PISA index
of economic, social
and cultural status (ESCS)
ESCS is a measure that combines
a variety of family background
characteristics (OECD, 2014). It is based
on pupils’ responses to questions about
their parents’ background and education,
and possessions in their homes. The
measure captures different elements of
social background such as economic
deprivation and the value a family
attributes to education
and educational
resources.
As noted above, all pupils benefit from Cognitive
Activation strategies in their maths lessons, however,
it appears that low and medium ESCS pupils profit
most from higher levels of Cognitive Activation. This is
particularly important as we know from previous analysis of
the England PISA 2012 data that pupils with lower ESCS scores
have, on average, lower maths achievement (Wheater et al., 2013).
As noted in the previous section it is lower ability pupils who report that their teachers
use Cognitive Activation strategies less frequently in their maths lessons. Given that the
evidence suggests it is exactly these pupils who will benefit most from undertaking these
strategies, teachers working with lower ability pupils should encourage them to summarise,
question, clarify and predict in order to solve even basic mathematical problems.
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PISA in Practice: Cognitive Activation in Maths
Cognitive Activation and pupil attitudes
to learning maths
PISA explores a wide range of pupil characteristics including family environment, learning
and thinking strategies, attitudes to school and learning, behaviour, motivation and beliefs.
Here we are focusing specifically on pupil attitudes to learning maths (measured in PISA by
motivation to learn maths and pupils’ beliefs in their own maths skills). There is a wealth of
research evidence to show that aspects of motivation, self-efficacy and self-concept are
more strongly correlated with achievement than other personality variables (Hattie, 2009).
Pupil attitudes are likely to be shaped by what happens in the classroom and therefore
it is important to explore whether there is a relationship between Cognitive Activation
and motivation, self-efficacy and self-concept. In addition, given that we have found that
Cognitive Activation is linked to maths achievement, it is important to establish whether
it has a negative relationship with these pupil attitudes, as this may influence a teacher’s
decision to use Cognitive Activation strategies in their maths lessons. Table 2 and Table 3
show the direction and strength of the relationship between Cognitive Activation and
motivation and beliefs for all pupils and each ESCS group.
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PISA in Practice: Cognitive Activation in Maths
Motivation to learn maths
‘Motivation and engagement can be regarded as
the driving forces behind learning.’ (OECD, 2013)
In PISA, motivation to learn maths is measured in terms of intrinsic motivation (based on a
pupil’s interest and enjoyment) and instrumental motivation (where learning maths is seen as
a useful activity). The OECD found that pupils who reported lower levels of interest in and
enjoyment of maths tended to have lower maths scores than pupils are more intrinsically
motivated. The same was true of instrumental motivation, with pupils who reported that
learning maths would help them in the future generally having higher maths achievement.
Pupils in England did not report a particularly high level of intrinsic motivation to learn
mathematics. However, they showed a greater level of instrumental motivation. For
example, nine out of 10 pupils in England said that learning maths is worthwhile because
it will improve career chances, compared with eight out of 10 on average internationally.
This suggests that although pupils in England do not find maths particularly interesting or
enjoyable they recognise that it is useful for their future (Wheater et al., 2013).
Table 2 Cognitive Activation and pupil attitudes to learning maths
All pupils
Low ESCS
pupils
Medium
ESCS pupils
High ESCS
pupils
+
+
+
+
+
+
+
+
Intrinsic motivation to
learn maths
Instrumental motivation
to learn maths
Shaded cells: statistically significant associations
Light blue cells indicate small associations; darker blue cells indicate medium associations
Table 2 shows that Cognitive Activation is positively related to both intrinsic and instrumental
motivation. In general these relationships are the same for pupils regardless of their socioeconomic status. This suggests that there is a link between how often pupils are asked to
use Cognitive Activation strategies to solve maths problems and their level of motivation to
learn maths. However, it is not possible to say for certain how this relationship works. We
do not know whether it is because pupils are motivated to learn maths that their teachers
use Cognitive Activation strategies more often or whether the opposite is true. That is,
do classrooms where teachers use Cognitive Activation strategies more frequently foster
beliefs that maths is more enjoyable and interesting and enable pupils to see importance of
learning maths for their careers?
Self-belief in maths skills
‘Mathematics self-beliefs have an impact on learning
and performance: cognitive, motivational, affective
and decision-making.’ (OECD, 2013)
Several aspects of self-belief were explored in PISA 2012, mathematics self-efficacy
(the extent to which pupils believe in their own ability to handle tasks and overcome
difficulties), mathematics self-concept (pupils’ beliefs in their own mathematics abilities)
and mathematics anxiety (thoughts and feeling about the self in relation to mathematics)
(OECD, 2013). The OECD found that on a country level maths self-efficacy, maths
self-concept and maths anxiety are strongly related to maths achievement.
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PISA in Practice: Cognitive Activation in Maths
In England, pupils showed generally positive self-beliefs and low anxiety about maths.
Pupils in England reported greater belief in their abilities in maths than was the case
internationally. For example, nearly three-quarters of pupils in England reported that they get
good marks in mathematics compared with less than two-thirds internationally. This greater
belief in ability is reflected in the level of anxiety reported, where pupils in England reported
less anxiety about maths lessons and tasks than pupils internationally (Wheater et al., 2013).
Table 3 Cognitive Activation and self-belief
All pupils
Maths self-efficacy
Maths self-concept
Maths anxiety
+
+
-
Low ESCS
pupils
+
+
-
Medium
ESCS pupils
+
+
-
High ESCS
pupils
+
+
-
Shaded cells: statistically significant associations
Light blue cells indicate small associations; darker blue cells indicate medium associations
Although Cognitive Activation is related to all three aspects of maths self-belief, the
relationship is strongest for self-efficacy (as shown in Table 3). In general the relationships
are weaker than those seen for intrinsic and instrumental motivation. However, the findings
still suggest that there is a link between how often pupils are asked to use Cognitive
Activation strategies to solve maths problems and their level of self-belief in their maths
skills. Again, it is not possible to say for certain how this relationship works. We do not know
whether it is because pupils are less anxious about maths that their teachers use Cognitive
Activation strategies more often or whether the opposite is true. That is, in classrooms
where teachers use Cognitive Activation strategies more frequently, pupils are less anxious
about maths.
The strength of the relationship between Cognitive Activation and self-efficacy and Cognitive
Activation and maths anxiety is different for pupils in the low ESCS group.
The relationship between Cognitive Activation and self-efficacy is stronger for pupils in the
lowest ESCS group. For this group of pupils, a higher level of Cognitive Activation in their
maths lessons is accompanied by higher self-efficacy. Therefore it appears that the use
of Cognitive Activation strategies in maths lessons may be particularly beneficial for this
group. We know from the PISA data that pupils in the lower ESCS groups are, on average,
the lower ability pupils and as identified in this report lower ability pupils are likely to use
Cognitive Activation strategies less frequently. However, given the potential benefit to these
particular pupils it is even more important that teachers try to use these strategies more
frequently in their maths lessons.
There is no relationship between the use of Cognitive Activation strategies and maths
anxiety for pupils in the low ESCS group compared with medium and high ESCS groups.
This means that a higher level of Cognitive Activation in their maths lessons is not
accompanied by lower maths anxiety. As anxiety has been found to be a barrier to learning
(Hattie, 2009), it is important that teachers consider using other teaching methods to help
reduce maths anxiety for this particular group of pupils.
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PISA in Practice: Cognitive Activation in Maths
Summary
Cognitive Activation appears to be an important teaching strategy that is positively
associated with maths achievement across all groups of pupils (regardless of ability or
socio-economic status).
This provides further evidence that teaching practices which challenge pupils to think and
reflect upon given mathematical problems and give them the opportunity to choose their
own procedures when faced with problems that have no obvious solution will foster pupils’
critical thinking about mathematics and have the potential to improve attainment. To provide
pupils with these opportunities, teachers will need to develop mathematical problems that
can be solved in different ways and may require different solutions in different contexts.
This kind of freedom in the learning process also requires a classroom climate where the
discussion of different solutions is encouraged and in which pupils are asked to explain
and defend their approaches and supports pupils to learn from their mistakes.
Cognitive Activation is only one of several practices that support the development of
mathematical literacy (OECD, 2013). It is reasonable to assume that it will be most effective
within a set of teaching practices that teachers use in order to meet the specific needs of
their class (Vieluf et al., 2012). This school effectiveness research suggests that Cognitive
Activation is most effective at enhancing pupil learning in combination with clear, wellstructured classroom management and a supportive, pupil-oriented classroom climate.
Page 15
PISA in Practice: Cognitive Activation in Maths
What can I do to increase
the amount of Cognitive
Activation in my lessons?
Here are some short-term, medium-term
and long-term strategies.
What could I do in my next lesson?
• Depending on your particular lesson focus or objective, try to relate the maths
context to a real life scenario, for example:
− How would a mathematician tile my bathroom?
− Is there enough food for everyone in the world? How could you work it out?
− What statistics do you come across in everyday life? Why is it important to
understand how to interpret statistics used in the media?
• Start to model key Cognitive Activation strategies and encourage pupils to
use these strategies as they solve problems individually and in small groups,
for example:
− Punctuate the class discussion with questions like: ‘What if…?’; ‘Does
everyone think that…?’; ‘Might there be an alternative way…?’
− Prompt pupils to provide more information to explain how they have
arrived at a particular solution to a problem: ‘Why did you choose that
method…?’; ‘Did you try any alternatives…?’
− Demonstrate thinking vocabulary: ‘I think…’; ‘because…’; ‘What do we do
next?’; ‘How do I check…?’
• Encourage and support collaborative work and talk for learning – provide
opportunities for groups to share ideas.
• Listen – be prepared to adapt your lesson plan. Use the evidence of what you
hear and see to ensure you are meeting learners where they are, differentiating
their range of learning needs.
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PISA in Practice: Cognitive Activation in Maths
What could I do next term?
• Seek out and explore ‘real life’ applications of the mathematical concepts you
are teaching.
• Speak to your pupils to identify the Cognitive Activation strategies that they find
the most difficult to use and explore why they find these particularly challenging.
Focus on these strategies during the term. Consider whether there are strategies
that are more difficult for particular groups of pupils.
• Encourage a culture of exploratory talk in your classroom where the goal is
not to produce a right or wrong answer – but where pupils consider a range
of possible solutions to problems and identify, for themselves, what they
need to learn.
• Encourage your pupils to identify how learning on a particular topic can be
applied in a range of situations and use their suggestions as a basis for planning
subsequent lessons.
• Record observations of where you see effective learning taking place as pupils
begin to become familiar with Cognitive Activation strategies (with a view to
sharing/discussing later with peers).
• Discuss with colleagues your observations of how the Cognitive Activation
strategies you are using with your class are working and any particular
difficulties you have had.
What could my maths department do next year?
• Consider collaborative planning to develop and share a range of Cognitive
Activation strategies. This will help to ensure they are being used across different
ability groups.
• All maths teachers could gather evidence of which strategies enhance learning
in their class and share this evidence within and across departments, identifying
if there are any strategies that work well for specific groups of pupils or for
particular topics.
• Ensure regular short updates (perhaps at staff meetings) so that colleagues
can continue to share, inspire and maintain awareness of the importance of
Cognitive Activation for enhancing learning. Use this forum to find success,
discuss difficulties and establish what makes it good practice.
• Share techniques and strategies on a whole-school level to help develop the use
of effective Cognitive Activation techniques across departments.
• Consider the development of interdisciplinary units where learning is linked
to real life situations across subject areas. For example, linking maths and
geography through a project to plan the layout of a town to minimise the
distances people travel to visit key community locations.
Page 17
NFER provides evidence for excellence through
its independence and insights, the breadth of its
work, its connections and a focus on outcomes.
References
Blaumert, J., Kunter, M., Blum, W., Brunner, M.,
Voss, T., Jordan, A., Klusmann, U., Krauss, S.,
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Brown, A.L. (1994). ‘The advancement of learning’,
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Hiebert, J. and Grouws, D.A. (2007). ‘The effects
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NFER ref. PQUK
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Framework: Mathematics, Reading, Science,
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[19 February 2015].
OECD (2014). PISA 2012 Results: What Students
Know and Can Do - Student Performance in
Mathematics, Reading and Science (Volume 1).
Paris: OECD Publishing [online]. Available: http://
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[19 February, 2015].
Vieluf, S., Kaplan, D., Klieme, E. and Bayer, S.
(2012). Teaching Practices and Pedagogical
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[19 February, 2015].
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(2014).Achievement of 15-Year-Olds in England:
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ISBN 978-1-910008-36-2
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